scholarly journals A GENERAL VISCOSITY APPROXIMATION METHOD OF FIXED POINT SOLUTIONS OF VARIATIONAL INEQUALITIES FOR NONEXPANSIVE SEMIGROUPS IN HILBERT SPACES

2008 ◽  
Vol 45 (4) ◽  
pp. 717-728 ◽  
Author(s):  
Somyot Plubtieng ◽  
Rattanaporn Wangkeeree
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Approximation Method ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups

scholarly journals The Meir-Keeler Type for Solving Variational Inequalities and Fixed Points of Nonexpansive Semigroups in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Phayap Katchang ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Strong Convergence Theorem ◽  
Accretive Mapping ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Nonexpansive Semigroups ◽  
Strongly Accretive Mapping

The aim of this paper is to introduce a new iterative scheme for finding common solutions of the variational inequalities for an inverse strongly accretive mapping and the solutions of fixed point problems for nonexpansive semigroups by using the modified viscosity approximation method associate with Meir-Keeler type mappings and obtain some strong convergence theorem in a Banach spaces under some parameters controlling conditions. Our results extend and improve the recent results of Li and Gu (2010), Wangkeeree and Preechasilp (2012), Yao and Maruster (2011), and many others.

scholarly journals A New Modified Hybrid Steepest-Descent by Using a Viscosity Approximation Method with a Weakly Contractive Mapping for a System of Equilibrium Problems and Fixed Point Problems with Minimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29 ◽  
Author(s):  
Uamporn Witthayarat ◽  
Thanyarat Jitpeera ◽  
Poom Kumam
Keyword(s):  
Fixed Point ◽  
Approximation Method ◽  
Contractive Mapping ◽  
Steepest Descent ◽  
Common Element ◽  
Viscosity Approximation Method ◽  
Viscosity Approximation ◽  
Weakly Contractive Mapping ◽  
Minimization Problems ◽  
Weakly Contractive

The purpose of this paper is to consider a modified hybrid steepest-descent method by using a viscosity approximation method with a weakly contractive mapping for finding the common element of the set of a common fixed point for an infinite family of nonexpansive mappings and the set of solutions of a system of an equilibrium problem. The sequence is generated from an arbitrary initial point which converges in norm to the unique solution of the variational inequality under some suitable conditions in a real Hilbert space. The results presented in this paper generalize and improve the results of Moudafi (2000), Marino and Xu (2006), Tian (2010), Saeidi (2010), and some others. Finally, we give an application to minimization problems and a numerical example which support our main theorem in the last part.

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